Transcript Workshop on NUCLEAR STRUCTURE AND DECAY DATA …

Decay Scheme Normalization
Jagdish K. Tuli
NNDC
Brookhaven National Laboratory
Upton, NY 11973, USA
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1.Relative intensity is what is generally
measured
2. Multipolarity and mixing ratio (d).
3. Internal Conversion Coefficients
• Theoretical Values:
•
From BRICC
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• Experimental values:
For very precise values ( 3% uncertainty).
Eg = 661 keV ; 137Cs (aK=0.0902 + 0.0008, M4)
Nuclear penetration effects.
233Pa b- decay to 233U.
Eg = 312 keV almost pure M1 from electron
sub-shell ratios.
However aK(exp) = 0.64 + 0.02.
(aK th(M1)=0.78, aK th(E2)=0.07)
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For mixed E0 transitions (e.g., M1+E0).
227Fr b- 227Ra
Eg = 379.1 keV (M1+E0); a(exp) = 2.4 + 0.8
ath(M1) = 0.40; ath(E2) = 0.08
½-
<10 ps
675.8
379.5
296.6
½227Ra
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Decay Scheme Normalization
Rel. Int.
Ig
It
Ib
Ie
Ia
Norm. Factor
NR  BR
NT  Br
NB  BR
NB  BR
NB  BR
Abs. Int.
%Ig
%It
%Ib
%Ie
%Ia
BR: Factor for Converting Intensity Per 100 Decays Through This
Decay Branch, to Intensity Per 100 Decays of the Parent Nucleus
NR: Factor for Converting Relative Ig to Ig Per 100 Decays Through
This Decay Branch.
NT: Factor for Converting Relative TI to TI Per 100 Decays Through
This Decay Branch.
NB: Factor for Converting Relative B- and E Intensities to Intensities
Per 100 Decays of This Decay Branch.
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Absolute intensities
“Intensities per 100 disintegrations of the parent
nucleus”
•
Measured (Photons from b-, e+b+, and a decay)
Simultaneous singles measurements
Coincidence measurements
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Normalization Procedures
1.
Absolute intensity of one gamma ray is known (%Ig)
b-
Ig1
Ig2
%Ig
Relative intensity Ig + DIg
Absolute intensity %Ig + D%Ig
Normalization factor N = %Ig / Ig
Uncertainty DN =[ (D%Ig/ %Ig)2+(DIg/ Ig)2]1/2 x N
Then %Igl = N x Igl
D%Igl = [(DN/N)2 + (DIg1/ Ig1)2]1/2 x Igl
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2.
From Decay Scheme
b- 100%
Ig
Ig: Relative g-ray intensity; a: total conversion coefficient
N x Ig x (1 + a) = 100%
Normalization factor
N = 100/ Ig x (1 + a)
Absolute g-ray intensity % Ig = N x Ig = 100/ (1 + a)
Uncertainty
D% Ig = 100 x Da/(1 + a)2
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Total intensity from transition-intensity balance
b-
200
Ig6
Ig5
Ig4
150
Ig2
Ig3
100
Ig7 95
Ig1
0
TI(g7) = TI(g5) + TI(g3)
If a(g7) is known, then
Ig7 = TI(g7) / [1 + a(g7)]
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Equilibrium Decay Chain
T0
A0
Ig1 T1
A1
T2
A2
Ig3
A3
T0 > T1, T2 are the radionuclide half-lives,
For t = 0 only radionuclide A0 exists,
% Ig3, Ig3, and Ig1 are known.
Then, at equilibrium
% Ig1 = (% Ig3/Ig3) × Ig1× (T0/(T0 – T1) × (T0/(T0 – T2)
Normalization factor
N = %Ig1/ Ig1
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b- 100%
Ig2
Ig3
Ig1
Normalization factor N = 100 / Ig1(1 + a1) + Ig3(1 + a3)
% Ig1 = N x Ig1 = 100 x Ig1 / Ig1(1 + a1) + Ig3(1 + a3)
% Ig3 = N x Ig3 = 100 x Ig3 / Ig1(1 + a1) + Ig3(1 + a3)
% Ig2 = N x Ig2 = 100 x Ig2 / Ig1(1 + a1) + Ig3(1 + a3)
Calculate uncertainties in %Ig1, % Ig2, and % Ig3. Use
3% fractional uncertainty in a1 and a3.
See Nucl. Instr. and Meth. A249, 461 (1986).
To save time use computer program GABS
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4.
Annihilation radiation intensity is known
e+b+
(g+ce) (in)
(g+ce)(out)
(e+b+)2
(e+b+)1
(e+b+)0
I(g+) = Relative annihilation radiation intensity
Xi = Intensity imbalance at the ith level = (g+ce) (out) – (g+ce) (in)
ri = ei / b+i theoretical ratio to ith level
Xi = ei + b+i = b+i (1 + ri), therefore b+i = Xi / 1 + ri
2 [X0 / (1 + r0) + Σ Xi / (1 + ri)] = I(g+) ……… (1)
[X0 + Σ Igi (g + ce) to gs ] N = 100 ………. (2)
Solve equation (1) for X0 (rel. gs feeding).
Solve equation (2) for N (normalization factor).
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5.
X-ray intensity is known
e+b+
(g+ce) (in)
(g+ce)(out)
(e+b+)2
(e+b+)1
(e+b+)0
IK = Relative Kx-ray intensity
Xi = Intensity imbalance at the ith level = (g+ce) (out) – (g+ce) (in)
ri = ei / b+i theoretical ratio to ith level
Xi = ei + b+i, so ei = Xi ri / 1 + ri (atomic vacancies); wK=Kfluorsc.yield
PKi = Fraction of the electron-capture decay from the K shell
IK= wK [e0×PK0 + Σ ei× PKi]
IK = wK [PK0× X0 r0 / (1 + r0) + Σ PKi× Xi ri / 1 + ri]…(1)
[X0 + Σ Ii(g + ce) to gs] N = 100 …. (2)
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Solve equation (1) for X , equation (2) for N.